x = linspace(-5, 5);
plot(x, 1./(1+x.^2), 'r');
hold on;
x = linspace(-8,-7);
plot(x,(2.299110473818736) + (0.862166427682026)*x.^1 + (0.1077708034602533)*x.^2 + (0.004490450144177219)*x.^3,'b');
hold on;
x = linspace(-7,-6);
plot(x,(-1.756652775395331) + (-0.8760178219811454)*x.^1 + (-0.1405412322059141)*x.^2 + (-0.007333932506592655)*x.^3,'b');
hold on;
x = linspace(-6,-5);
plot(x,(0.7952675119857763) + (0.399942321709408)*x.^1 + (0.07211879174251148)*x.^2 + (0.004480513268319877)*x.^3,'b');
hold on;
x = linspace(-5,-4);
plot(x,(0.3174532064744031) + (0.1132537384025842)*x.^1 + (0.01478107508114672)*x.^2 + (0.0006579988242288934)*x.^3,'b');
hold on;
x = linspace(-4,-3);
plot(x,(0.7682884869357846) + (0.4513801987486197)*x.^1 + (0.09931269016765554)*x.^2 + (0.007702300081437956)*x.^3,'b');
hold on;
x = linspace(-3,-2);
plot(x,(0.7369563515788831) + (0.420048063391718)*x.^1 + (0.08886864504868813)*x.^2 + (0.006541850623774909)*x.^3,'b');
hold on;
x = linspace(-2,-1);
plot(x,(1.543075690682258) + (1.629227072046788)*x.^1 + (0.6934581493762246)*x.^2 + (0.1073067680116977)*x.^3,'b');
hold on;
x = linspace(-1,0);
plot(x,(0.9999999999999432) + (-7.105427357601002e-15)*x.^1 + (-0.935768922670567)*x.^2 + (-0.4357689226705659)*x.^3,'b');
hold on;
x = linspace(0,1);
plot(x,(0.9999999999998721) + (-2.842170943040401e-14)*x.^1 + (-0.9357689226705679)*x.^2 + (0.4357689226705659)*x.^3,'b');
hold on;
x = linspace(1,2);
plot(x,(1.543075690682233) + (-1.629227072046797)*x.^1 + (0.6934581493762253)*x.^2 + (-0.1073067680116978)*x.^3,'b');
hold on;
x = linspace(2,3);
plot(x,(0.7369563515788888) + (-0.4200480633917114)*x.^1 + (0.08886864504868799)*x.^2 + (-0.006541850623774857)*x.^3,'b');
hold on;
x = linspace(3,4);
plot(x,(0.7682884869357915) + (-0.4513801987486187)*x.^1 + (0.0993126901676557)*x.^2 + (-0.007702300081437968)*x.^3,'b');
hold on;
x = linspace(4,5);
plot(x,(0.3174532064744098) + (-0.1132537384025826)*x.^1 + (0.01478107508114677)*x.^2 + (-0.0006579988242288951)*x.^3,'b');
hold on;
x = linspace(5,6);
plot(x,(0.7952675119857799) + (-0.3999423217094074)*x.^1 + (0.07211879174251146)*x.^2 + (-0.004480513268319873)*x.^3,'b');
hold on;
x = linspace(6,7);
plot(x,(-1.756652775395339) + (0.8760178219811443)*x.^1 + (-0.1405412322059141)*x.^2 + (0.007333932506592655)*x.^3,'b');
hold on;
x = linspace(7,8);
plot(x,(2.299110473818736) + (-0.862166427682026)*x.^1 + (0.1077708034602533)*x.^2 + (-0.004490450144177219)*x.^3,'b');
hold on;
